I was messing around with computing the "cost" of running functional programs a while back. For example, an expression like \$$5\$$ would have a cost of \$$0\$$, an expression like \$$2 + 3\$$ would have a cost of \$$1\$$, and a non-terminating expression would have a cost of \$$\infty\$$. It seems that this is related to a \$$\mathbf{Cost}\$$-enriched category where \$$\mathrm{Ob}(\mathcal{X})\$$ is the set of terms and \$$\mathcal{X}(x,y)\$$ is the minimum possible number of steps to reduce x to y under all possible reduction strategies, which might be \$$\infty\$$. Is this an accurate example?